Lesson 3 Fried Freddy’s Solidify Understanding

Ready

In some of the situations described below, the first event affects the subsequent event (dependent events). In other situations, the two events are completely independent (independent events). Determine which situations are dependent and which are independent.

1.

A coin is flipped twice. The first event is the first flip, and the second event is the next flip.

A.

Dependent events

B.

Independent events

2.

A bag of marbles contains $3$ blue marbles, $6$ red marbles, and $2$ yellow marbles. Two of the marbles are drawn out of the bag. The first event is the first marble taken out and not returned to the bag. The second event is the second marble taken out.

A.

Dependent events

B.

Independent events

3.

A batter’s swing is either right-handed or left-handed. The first event is the first batter to come to the plate. The second event is the second batter to come up to the plate.

A.

Dependent events

B.

Independent events

4.

A standard die is rolled twice. The first event is the first roll and the second event is the second roll.

A.

Dependent events

B.

Independent events

5.

Two cards are drawn from a standard deck of cards. The first event is the first card that is drawn and not returned to the deck. The second event is the second card that is drawn.

A.

Dependent events

B.

Independent events

Set

6.

Sally was assigned to create a Venn diagram to represent $P (A or B)$ . Sally first writes $P (A or B) = P (A) + P (B) - P (A and B)$ ; what does this mean? Explain each part.

7.

Sally then creates the following diagram.

Sally’s Venn diagram is incorrect. Why?

The Venn diagram shows the data collected at a sandwich shop for the last six months. It shows the type of bread people ordered (sourdough or wheat) and whether or not they got cheese on their sandwich. Use this data to create a two-way frequency table and answer the problems.

8.

Two-way frequency table.

9.

What is the probability that a randomly selected customer would order sourdough bread?

$P (sourdough bread) =$

10.

What is the probability that a randomly selected customer would order sourdough bread without cheese?

$P (sourdough \cap no cheese) = P (sourdough and no cheese) =$

11.

What is the probability that a person prefers wheat bread without cheese?

$P (wheat \cap no cheese) = P (wheat and no cheese) =$

12.

What is the estimated probability that a randomly selected customer would want their sandwich with cheese?

$P (sourdough cheese and wheat cheese) = P ($ $\underset{―}{}$ $) =$

13.

If they serve $100$ sandwiches at lunch on a particular day, how many orders with sourdough should be prepared without cheese?

14.

What is the probability that a randomly selected person would choose sourdough or no cheese?

$P (sourdough \cup no cheese) = P (sourdough or no cheese) =$

15.

What is the probability that a randomly selected person would NOT choose sourdourgh or no cheese?

Go

Use the given ratio to set up a proportion and find the desired value.

16.

If $3$ out of $5$ students eat school lunch, then how many students would be expected to eat school lunch at a school with $750$ students?

17.

In a survey, it was found that $6$ out of $10$ students have a pair of sunglasses. How many students would you expect to have a pair of sunglasses out of a group of $45$ students?

18.

Data collected at a local mall indicated that $7$ out of $20$ men observed were wearing a hat. How many men would you expect to be wearing hats if $7,500$ men were at the mall on a similar day?